In the design and fabrication of electrical and electronic components, there is often a need for measuring the sheet resistance of a fabricated material. In the design of a semiconductor integrated circuit, the sheet resistance of materials fabricated on the integrated circuit is often needed for process and device characterization. For example, sheet resistance is commonly used to evaluate the outcome of semiconductor doping operations. The sheet resistance can be needed for any material or device that is fabricated on the integrated circuit.
The following example shows one method of defining sheet resistance. If a rectangular block of uniformly doped material has a resistively p, a length L, and a cross-sectional area A, then the resistance of the rectangular block can be expressed as,                     R        =                  ρ          ⁢                      L            A                                              EQ        .                                   ⁢        1            
If the rectangular block has a width W and thickness t, then the resistance can be rewritten                     R        =                                            ρ              t                        ×                          L              W                                =                      Rs            ⁢                          L              W                                                          EQ        .                                   ⁢        2            where Rs=ρ/t is the sheet resistance in ohms of a layer of the material of the block. However, sheet resistance is often expressed in units of “omhs per square,” where L/W is the number of units squares of the material. Therefore, if the sheet resistance of the material is known, the resistance of a particular device formed of that material can be calculated from the number of “squares” of the material in the body of the device.
The typical method of measuring sheet resistance is analog in nature. A known current is inserted into the resistor and the voltages across the resistor are measured so that the sheet resistance for the material can be determined. In the Van der Pauw method, resistively of a semiconductor is measured by using four probes (contacts) located arbitrarily on the surface of the material. Alternate contacts are used to measure two sets of current-voltage characteristics and then a value of the resistively is extracted from a formula.
These analog-type methods are rather slow and complex and often require physical access to the material being tested. Improved methods and apparatus for measuring sheet resistance of a material are therefore desired.